Yes, but I wonder how much power it would need and if the alternator could deliver it, given
's comment about relative sizes.
The Pacifica, like most modern cars, consumes a LOT of power even before the headlights come on, (and this is a possible design deficit) it may not have a strong enough alternator to cope with multiple slow, short trips, and the ESS charging load probably exacerbates that situation.
At least ESS shuts itself off when it detects a low battery. With almost instant starting thanks to fuel injection, we lost the clue of slow cranking that used to warn us when a main battery struggles.
I don't have ESS, but I can see that keeping lights, fans, radios, etc. going when the engine is off is not a trivial load. I also suspect that ESS batteries have a much deeper charge/discharge history than the main battery. And perhaps those deep discharges shorten the life. I know that when my van would not start with a flat battery (the only warning was the infotainment screen was dead all day -- the van started fine on several trips, and then would not even operate the sliding door the next morning) based on comments here I insisted on new battery. According to posts in the forums, a discharge that deep drastically cuts the life of the battery. I don't know if the ESS cuts out fast enough to prevent damage to the battery.
There is a constant stream of early battery replacement posts in these threads (including mine at about 20 months, and comments that Chrysler is not alone in this trend. Maybe those who monitor other brands can verify this.